Wahrscheinlich vs. wohl says that "warscheinlich" and "wohl" are interchangeable when they mean "probably". However, I have been told that the following 2 sentences do not mean exactly the same.
Is that correct?
It is always difficult to describe such minor differences because there is alsways the possibility that in different regions or social groups the words are used differently, but my explanation would be, that it is more opposite to the original version of your guess.
Du bist wahrscheinlich müde
sounds like a conclusion based on information (it's 23:00 and I know you got up at 5:30 and did a lot of work today), while
Du bist wohl müde
sounds like an observation (you are yawning a lot).
Yes, that's just it. "wohl" is only used when you infer something from something you've observed. But "wahrscheinlich" can also describe the situation where you assume something just from general principles, such as "People are generally tired late at night".
Prototypical examples:
Ich finde, Donatello ist die coolste Ninja Turtle. - Du bist wohl nicht bei Trost!!
Sei gegrüsst, unbekannter Leser! Wahrscheinlich wunderst Du Dich, wer am Boden des Marianengraben einen Geocache hinterlegt hat...
... ?Du bist wahrscheinlich nicht bei Trost! [Sounds strange, too neutral for the conversational setting.]
Du wunderst Dich wohl, wer... [acceptable - it indicates that the hider is engaging in an imaginary conversation with the future finder.]
